process systems analysis and control third edition

Coughanowr
LeBlanc
Third
Edition
Process Systems
Analysis and Control
Process Systems
Analysis and Control
Donald R. Coughanowr
Steven E. LeBlanc
Third Edition
Process Systems Analysis and Control, Third Edition retains the clarity of presentation for which
this book is well known. It is an ideal teaching and learning tool for a semester-long undergraduate
chemical engineering course in process dynamics and control. It avoids the encyclopedic approach
of many other texts on this topic. Computer examples using MATLAB
¨
and Simulink
¨
have been
introduced throughout the book to supplement and enhance standard hand-solved examples. These
packages allow the easy construction of block diagrams and quick analysis of control concepts to enable
the student to explore Òwhat-ifÓ type problems that would be much more difcult and time consuming
by hand. New homework problems have been added to each chapter. The new problems are a mixture
of hand-solutions and computational-exercises. One-page capsule summaries have been added to the
end of each chapter to help students review and study the most important concepts in each chapter.
Key Features:
control classesÉthat this is just another mathematics course disguised as an engineering course
¨ ¨
and Excel
¨
have been introduced throughout the

book.
dynamics and control and not get bogged down in the mathematical complexities of each problem
available for the course material
The Solutions to the End-of-Chapter Problems are available to Instructors at the textÕs website:
www.mhhe.com/coughanowr-leblanc
Electronic Textbook Options
This text is offered through CourseSmart for both instructors and students. CourseSmart is an online
browser where students can purchase access to this and other McGraw-Hill textbooks in a digital
half the cost of a traditional text. Purchasing the eTextbook also allows students to take advantage of
sales representative or visit
www.CourseSmart.com.
ISBN 978-0-07-339789-4
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PROCESS SYSTEMS ANALYSIS
AND CONTROL
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McGraw-Hill Chemical Engineering Series
Editorial Advisory Board
Eduardo D. Glandt, Dean, School of Engineering and Applied Science, University of
Pennsylvania
Michael T. Klein, Dean, School of Engineering, Rutgers University
Thomas F. Edgar, Professor of Chemical Engineering, University of Texas at Austin
Coughanowr and LeBlanc: Process Systems Analysis and Control
Davis and Davis: Fundamentals of Chemical Reaction

Engineering
de Nevers: Air Pollution Control Engineering
de Nevers: Fluid Mechanics for Chemical Engineers
Douglas: Conceptual Design of Chemical Processes
Edgar, Himmelblau, and Lasdon: Optimization of Chemical Processes
Marlin: Process Control
McCabe, Smith, and Harriott: Unit Operations of Chemical Engineering
Murphy: Introduction to Chemical Processes
Perry and Green: Perry’s Chemical Engineers’ Handbook
Peters, Timmerhaus, and West: Plant Design and Economics for
Chemical Engineers
Smith, Van Ness, and Abbott: Introduction to Chemical Engineering
Thermodynamics
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The Founding of a Discipline:
The McGraw-Hill Companies, Inc. Series in Chemical Engineering
Over 80 years ago, 15 prominent chemical engineers met in New York to plan a con-
tinuing literature for their rapidly growing profession. From industry came such pioneer
practitioners as Leo H. Baekeland, Arthur D. Little, Charles L. Reese, John V. N. Dorr,
M. C. Whitaker, and R. S. McBride. From the universities came such eminent educa-
tors as William H. Walker, Alfred H. White, D. D. Jackson, J. H. James, Warren K.
Lewis, and Harry A. Curtis. H. C. Parmlee, then editor of Chemical and Metallurgical
Engineering, served as chairman and was joined subsequently by S. D. Kirkpatrick as
consulting editor.
After several meetings, this committee submitted its report to the McGraw-Hill
Book Company in September 1925. In the report were detailed specifi cations for a
correlated series of more than a dozen texts and reference books which became the
McGraw-Hill Series in Chemical Engineering—and in turn became the cornerstone of
the chemical engineering curricula.

From this beginning, a series of texts has evolved, surpassing the scope and lon-
gevity envisioned by the founding Editorial Board. The McGraw-Hill Series in Chemi-
cal Engineering stands as a unique historical record of the development of chemical
engineering education and practice. In the series one fi nds milestones of the subject’s
evolution: industrial chemistry, stoichiometry, unit operations and processes, thermo-
dynamics, kinetics, and transfer operations.
Textbooks such as McCabe et al., Unit Operations of Chemical Engineering,
Smith et al., Introduction to Chemical Engineering Thermodynamics, and Peters et al.,
Plant Design and Economics for Chemical Engineers have taught to generations of
students the principles that are key to success in chemical engineering.
Chemical engineering is a dynamic profession, and its literature continues to
grow. McGraw-Hill, with its in-house editors and consulting editors Eduardo Glandt
(Dean, University of Pennsylvania), Michael Klein (Dean, Rutgers University), and
Thomas Edgar (Professor, University of Texas at Austin), remains committed to a pub-
lishing policy that will serve the needs of the global chemical engineering profession
throughout the years to come.
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PROCESS SYSTEMS
ANALYSIS AND CONTROL
THIRD EDITION
Steven E. LeBlanc
Chemical Engineering University of Toledo
Donald R. Coughanowr
Emeritus Professor, Chemical Engineering Drexel University
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PROCESS SYSTEMS ANALYSIS AND CONTROL, THIRD EDITION
Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY
10020. Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 1991 and 1965. No

part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system,
without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other
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Some ancillaries, including electronic and print components, may not be available to customers outside the United States.
This book is printed on acid-free paper.
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ISBN 978–0–07–339789–4
MHID 0–07–339789–X
Global Publisher: Raghothaman Srinivasan
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Library of Congress Cataloging-in-Publication Data
Coughanowr, Donald R.
Process systems analysis and control.—3rd ed. / Donald R. Coughanowr, Steven E. LeBlanc.
p. cm.—(Mcgraw-Hill chemical engineering series)
Includes index.
ISBN 978–0–07–339789–4—ISBN 0–07–339789–X (hard copy : alk. paper) 1. Chemical process control. I. LeBlanc,
Steven E. II. Title.
TP155.75.C68 2009
660'.2815—dc22 2008018252
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Dedication
For Molly, my children, and grandchildren . . .
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ix
CONTENTS
Preface to the Third Edition xv
Chapter 1 Introductory Concepts 1
1.1 Why Process Control? 1
1.2 Control Systems 1
PART I MODELING FOR PROCESS DYNAMICS 9
Chapter 2 Modeling Tools for Process Dynamics 11
2.1 Process Dynamics—A Chemical Mixing Scenario 11
2.2 Mathematical Tools for Modeling 18
2.3 Solution of Ordinary Differential Equations (ODEs) 26
Chapter 3 Inversion by Partial Fractions 32
3.1 Partial Fractions 32
3.2 Qualitative Nature of Solutions 43
Appendix 3A: Further Properties of Transforms and Partial Fractions 49
PART II LINEAR OPEN-LOOP SYSTEMS 69
Chapter 4 Response of First-Order Systems 71
4.1 Transfer Function 71
4.2 Transient Response 77
4.3 Forcing Functions 78
4.4 Step Response 79
4.5 Impulse Response 84
4.6 Ramp Response 87
4.7 Sinusoidal Response 87

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Chapter 5 Physical Examples of First-Order Systems 99
5.1 Examples of First-Order Systems 99
5.2 Linearization 109
Chapter 6 Response of First-Order Systems in Series 123
6.1 Introductory Remarks 123
6.2 Noninteracting System 123
6.3 Interacting System 128
Chapter 7 Higher-Order Systems: Second-Order
and Transportation Lag
137
7.1 Second-Order System 137
7.2 Transportation Lag 153
PART III LINEAR CLOSED-LOOP SYSTEMS 163
Chapter 8 The Control System 165
8.1 Introduction 165
8.2 Components of a Control System 165
8.3 Block Diagram 166
8.4 Development of Block Diagram 168
Chapter 9 Controllers and Final Control Elements 186
9.1 Mechanisms 187
9.2 Ideal Transfer Functions 190
Appendix 9A: Piping and Instrumentation Diagram Symbols 203
Chapter 10 Block Diagram of a Chemical-Reactor
Control System
205
10.1 Description of System 206
10.2 Reactor Transfer Functions 206

10.3 Control Valve 209
10.4 Measuring Element 210
10.5 Controller 211
10.6 Controller Transducer 212
10.7 Transportation Lag 212
10.8 Block Diagram 212
Chapter 11 Closed-Loop Transfer Functions 218
11.1 Standard Block-Diagram Symbols 218
11.2 Overall Transfer Function for Single-Loop Systems 219
11.3 Overall Transfer Function for Multiloop Control Systems 224
x
CONTENTS
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Chapter 12 Transient Response of Simple
Control Systems
228
12.1 Proportional Control for Set Point Change
(Servo Problem—Set Point Tracking)
229
12.2 Proportional Control for Load Change (Regulator
Problem—Disturbance Rejection)
234
12.3 Proportional-Integral Control for Load Change 236
12.4 Proportional-Integral Control for Set Point Change 241
12.5 Proportional Control of System with Measurement Lag 243
Chapter 13 Stability 252
13.1 Concept of Stability 252
13.2 Defi nition of Stability (Linear Systems) 254

13.3 Stability Criterion 254
13.4 Routh Test for Stability 258
Chapter 14 Root Locus 269
14.1 Concept of Root Locus 269
PART IV FREQUENCY RESPONSE 285
Chapter 15 Introduction to Frequency Response 287
15.1 Substitution Rule 287
15.2 Bode Diagrams 300
15.3 Appendix—Generalization of Substitution Rule 316
Chapter 16 Control System Design by Frequency Response 323
16.1 Tank Temperature Control System 323
16.2 The Bode Stability Criterion 326
16.3 Gain and Phase Margins 327
16.4 Ziegler-Nichols Controller Settings 335

PART V PROCESS APPLICATIONS 351
Chapter 17 Advanced Control Strategies 353
17.1 Cascade Control 353
17.2 Feedforward Control 361
17.3 Ratio Control 370
17.4 Dead-Time Compensation (Smith Predictor) 373
17.5 Internal Model Control 378
CONTENTS xi
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Chapter 18 Controller Tuning and Process Identifi cation 391
18.1 Controller Tuning 391
18.2 Tuning Rules 394
18.3 Process Identifi cation 410

Chapter 19 Control Valves 423
19.1 Control Valve Construction 423
19.2 Valve Sizing 425
19.3 Valve Characteristics 427
19.4 Valve Positioner 438
Chapter 20 Theoretical Analysis of Complex Processes 443
20.1 Control of a Steam-Jacketed Kettle 443
20.2 Dynamic Response of a Gas Absorber 453
20.3 Distributed-Parameter Systems 458
PART VI STATE-SPACE METHODS 475
Chapter 21 State-Space Representation of Physical Systems 477
21.1 Introduction 477
21.2 State Variables 477
Appendix 21A: Elementary Matrix Algebra 490
Chapter 22 Transfer Function Matrix 498
22.1 Transition Matrix 499
22.2 Transfer Function Matrix 502
Chapter 23 Multivariable Control 512
23.1 Control of Interacting Systems 514
23.2 Stability of Multivariable Systems 525
PART VII NONLINEAR CONTROL 531
Chapter 24 Examples of Nonlinear Systems 533
24.1 Defi nition of a Nonlinear System 533
24.2 The Phase Plane 534
24.3 Phase-Plane Analysis of Damped Oscillator 535
24.4 Motion of a Pendulum 543
24.5 A Chemical Reactor 547
Chapter 25 Examples of Phase-Plane Analysis 553
25.1 Phase Space 553
25.2 Examples of Phase-Plane Analysis 561

xii
CONTENTS
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PART VIII COMPUTERS IN PROCESS CONTROL 579
Chapter 26 Microprocessor-Based Controllers
and Distributed Control
581
26.1 Historical Background 581
26.2 Hardware Components 582
26.3 Tasks of a Microprocessor-Based Controller 583
26.4 Special Features of Microprocessor-Based Controllers 588
26.5 Distributed Control 592
Bibliography 597
Index 599
CONTENTS xiii
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xv
PREFACE TO THE THIRD EDITION
I t has been over 17 years since the second edition of this book was published. The sec-
ond edition, which was written by Dr. Donald R. Coughanowr in 1991, contained many
changes and new topics to bring the book up to date at the time of publication. The third
edition has been a number of years in the making. I would like to thank Dr. Coughanowr
for the opportunity to work on this project and help update this excellent work, which
he fi rst published in 1965 with Dr. Lowell B. Koppel. As an undergraduate, I learned
process control from the fi rst edition of this text over 30 years ago. It was an excellent
book then, and it still is. I’ve used a number of other books over the years as a student

and as a professor, but I kept coming back to this one. I felt that it was the best book
to learn from. Is it an all-encompassing, totally comprehensive process dynamics and
control book? No, but it is not intended to be. It is a clearly written book that is geared
toward students in a fi rst process dynamics and control course. Many control books
on the market contain more material than one could ever hope to cover in a standard
undergraduate semester-long class. They can be overwhelming and diffi cult to learn
from. I have always felt that one of the strengths of this book, from both the student’s
and professor’s point of view, was the relatively short, easy-to-read chapters that can be
covered in one to two lectures. An additional strength of this text has been its unique
ability to be a teaching and learning text. I hope that in this current revision, I have been
able to retain that style and fl avor, while introducing some new material and examples
to update the text.
OBJECTIVES AND USES OF THE TEXT
This text is intended for use in an introductory one-semester-long undergraduate proc-
ess dynamics and control course. It is intended to be not a comprehensive treatise on
process control, but rather a textbook that provides students with the tools to learn
the basic material and be in a position to continue their studies in the area if they so
choose. Students are expected to have a background in mathematics through differ-
ential equations, material and energy balance concepts, and unit operations. After the
fi rst 13 chapters, the instructor may select from the remaining chapters to fi t a course
of particular duration and scope. A typical one-semester 15-week course, for example,
may include Chapters 1 through 19 and 26.
Features of the third edition
• A capsule summary of the important points at the end of each chapter
• Restructuring of the initial chapters to reduce the impression that students fre-
quently have regarding control classes—that this is just another mathematics
course disguised as an engineering course
• Integration of MATLAB,
®
Simulink,

®
and Excel throughout the text:
• To reduce the tedium of solving problems so that students may concentrate
more on the concepts of dynamics and control and not get bogged down in the
mathematical complexities of each problem
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• To give students the tools to be able to ask (and more easily answer) “what if . . .?”
type of questions
• To allow students to explore more difficult problems than would otherwise be
possible in the time available for the course material
ACKNOWLEDGMENTS
We would like to thank the following reviewers of the third edition for their help-
ful comments and suggestions: Thomas F. Edgar, University of Texas–Austin; John
Erjavec, University of North Dakota; Duane Johnson, University of Alabama; Costas
Maranas, Penn State University; Michael Nikolaou, University of Houston; F. Joseph
Schork, Georgia Institute of Technology; Delmar Timm, University of Nebraska; and
William A. Weigand, University of Maryland. We especially acknowledge the helpful
suggestions from Susan Montgomery of the University of Michigan and thank her for
her thoroughness and useful comments to help make the text more student-friendly.
I would like to thank McGraw-Hill for having confi dence in this project and
providing the opportunity to revise and update the text. Special thanks go to Lorraine
Buczek, Developmental Editor, and Melissa Leick, Project Manager, for their help in
the fi nal stages of this revision.
I would also like to thank my students and my University of Toledo colleague
Sasidhar Varanasi for his help in using manuscript drafts when he taught the Process
Control course to “fi eld-test” the revisions. I am also grateful to my friend and colleague
Dean Nagi Naganathan, of the College of Engineering at the University of Toledo, for
his general support and his willingness to allow me the time required to complete this
work. I especially want to thank my wife, Molly, for her love and continuing encourage-

ment and support over the course of the writing and revising.
Dr. Steven E. LeBlanc
University of Toledo
RESOURCES FOR INSTRUCTORS AND STUDENTS:
For instructors, the solutions to the end-of-chapter problems are available at the text’s
website: www.mhhe.com/coughanowr-leblanc
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xvi
PREFACE TO THE THIRD EDITION
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xvii
HISTORY OF PROCESS SYSTEMS
ANALYSIS AND CONTROL (FROM
THE SECOND EDITION PREFACE)
Since the fi rst edition of this book was published in 1965, many changes have taken
place in process control. Nearly all undergraduate students in chemical engineering are
now required to take a course in process dynamics and control. The purpose of this
book is to take the student from the basic mathematics to a variety of design applica-
tions in a clear, concise manner.
The most signifi cant change since the fi rst edition is the use of the digital compu-
ter in complex problem solving and in process control instrumentation. However, the

fundamentals of process control, which remain the same, must be acquired before one
can appreciate the advanced topics of control.
In its present form, this book represents a major revision of the fi rst edition. The
material for this book evolved from courses taught at Purdue University and Drexel
University. The fi rst 17 chapters on fundamentals are quite close to the fi rst 20 chapters
of the fi rst edition. The remaining 18 chapters contain many new topics, which were
considered very advanced when the fi rst edition was published.
Knowledge of calculus, unit operations, and complex numbers is presumed on the
part of the student. In certain later chapters, more advanced mathematical preparation is
useful. Some examples would include partial differential equations in Chap. 21, linear
algebra in Chaps. 28 through 30, and Fourier series in Chap. 33.
Analog computation and pneumatic controllers in the fi rst edition have been
replaced by digital computation and microprocessor-based controllers in Chaps. 34
and 35. The student should be assigned material from these chapters at the appropriate
time in the development of the fundamentals. For example, the transient response for a
system containing a transport lag can be obtained easily only with the use of computer
simulation of the transport lag. Some of the software now available for solving control
problems should be available to the student; such software is described in Chap. 34.
To understand the operation of modern microprocessor-based controllers, the student
should have hands-on experience with these instruments in a laboratory.
Chapter 1 is intended to meet one of the problems consistently faced in present-
ing this material to chemical engineering students, that is, one of perspective. The
methods of analysis used in the control area are so different from the previous experi-
ences of students that the material comes to be regarded as a sequence of special math-
ematical techniques, rather than an integrated design approach to a class of real and
practically signifi cant industrial problems. Therefore, this chapter presents an overall,
albeit superfi cial, look at a simple control system design problem. The body of the
text covers the following topics: Laplace transforms, Chaps 2. to 4; transfer functions
and responses of open-loop systems, Chaps. 5 to 8; basic techniques of closed-loop
control, Chaps. 9 to 13; stability, Chap. 14; root locus methods, Chap. 15; frequency

response methods and design, Chaps. 16 and 17; advanced control strategies (cascade,
feedforward, Smith predictor, internal model control), Chap. 18; controller tuning and
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process identifi cation, Chap. 19; control valves, Chap. 20; advanced process dynam-
ics, Chap. 21; sampled-data control, Chaps. 22 to 27; state-space methods and multi-
variable control, Chaps. 28 to 30; nonlinear control, Chaps. 31 to 33; digital computer
simulation, Chap. 34; microprocessor-based controllers, Chap. 35.
It has been my experience that the book covers suffi cient material for a one-
semester (15-week) undergraduate course and an elective undergraduate course or part
of a graduate course. In a lecture course meeting 3 hours per week during a 10-week
term, I have covered the following chapters: 1 to 10, 12 to 14, 16, 17, 20, 34, and 35.
After the fi rst 14 chapters, the instructor may select the remaining chapters to fi t
a course of particular duration and scope. The chapters on the more advanced topics
are written in a logical order; however, some can be skipped without creating a gap in
understanding.
I gratefully acknowledge the support and encouragement of the Drexel University
Department of Chemical Engineering for fostering the evolution of this text in its cur-
riculum and for providing clerical staff and supplies for several editions of class notes. I
want to acknowledge Dr. Lowell B. Koppel’s important contribution as coauthor of the
fi rst edition of this book. I also want to thank my colleague Dr. Rajakannu Mutharasan
for his most helpful discussions and suggestions and for his sharing of some of the new
problems. For her assistance in typing, I want to thank Dorothy Porter. Helpful sug-
gestions were also provided by Drexel students, in particular Russell Anderson, Joseph
Hahn, and Barbara Hayden. I also want to thank my wife Effi e for helping me check the
page proofs by reading to me the manuscript, the subject matter of which is far removed
from her specialty of Greek and Latin.
McGraw-Hill and I would like to thank Ali Cinar, Illinois Institute of Technology;
Joshua S. Dranoff, Northwestern University; H. R. Heichelheim, Texas Tech University;
and James H. McMicking, Wayne State University, for their many helpful comments

and suggestions in reviewing this second edition.
Dr. Donald R. Coughanowr

xviii HISTORY OF PROCESS SYSTEMS ANALYSIS AND CONTROL (FROM THE SECOND EDITION PREFACE)
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xix
ABOUT THE AUTHORS
Steven E. LeBlanc is Associate Dean for Academic Affairs and professor of chemical
engineering at the University of Toledo. He received a B.S. degree in chemical engi-
neering from the University of Toledo and his M.S. and Ph.D. in chemical engineering
from the University of Michigan. He joined the faculty at the University of Toledo in
1980. He served as the department chair for the Department of Chemical and Envi-
ronmental Engineering from 1993 to 2003, when he became an Associate Dean in the
College of Engineering.
Dr. LeBlanc’s industrial experience includes power plant process system design
and review for Toledo Edison Company (now a division of First Energy). He has taught
the Process Dynamics and Control course numerous times, and was responsible for a
major revamp of laboratory activities associated with the course.
He is a member of the American Institute of Chemical Engineers (AIChE) and
the American Society for Engineering Education (ASEE). He has served as an ABET
chemical engineering program evaluator for AIChE since 1998. He chaired the national
ASEE Chemical Engineering Education Division and cochaired the 2007 ASEE Chemi-
cal Engineering Summer School for Faculty. He coauthored and judged the 1992 AIChE
Senior Design Project competition. He is also coauthor of a textbook on Strategies for
Creative Problem Solving with H. Scott Fogler of the University of Michigan.
Donald R. Coughanowr is Emeritus Professor of Chemical Engineering at
Drexel University. In 1991 he wrote the second edition of Process Systems Analysis
and Control which contained many changes and new topics in order to bring the book
up to date at the time of publication. He received a Ph.D. in chemical engineering from

the University of Illinois in 1956, an M.S. degree in chemical engineering from the
University of Pennsylvania in 1951, and a B.S. degree in chemical engineering from the
Rose-Hulman Institute of Technology in 1949. He joined the faculty at Drexel Univer-
sity in 1967 as department head, a position he held until 1988. Before going to Drexel,
he was a faculty member of the School of Chemical Engineering at Purdue University
for 11 years.
At Drexel and Purdue he taught a wide variety of courses, which include
material and energy balances, thermodynamics, unit operations, transport phenom-
ena, petroleum refi nery engineering, environmental engineering, chemical engineer-
ing laboratory, applied mathematics, and process dynamics and control. At Purdue,
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he developed a new course and laboratory in process control and collaborated with
Dr. Lowell B. Koppel on the writing of the fi rst edition of Process Systems Analysis
and Control.
His research interests included environmental engineering, diffusion with chemi-
cal reaction, and process dynamics and control. Much of his research in control empha-
sized the development and evaluation of new control algorithms for the processes that
cannot be controlled easily by conventional control; some of the areas investigated
were time-optimal control, adaptive pH control, direct digital control, and batch control
of fermentors. He reported on his research in numerous publications and received sup-
port for research projects from the National Science Foundation and industry. He spent
sabbatical leaves teaching and writing at Case-Western Reserve University, the Swiss
Federal Institute, the University of Canterbury, the University of New South Wales, the
University of Queensland, and Lehigh University.
Dr. Coughanowr’s industrial experience included process design and pilot plant
at Standard Oil Co. (Indiana) and summer employment at Electronic Associates and
Dow Chemical Company.
He is a member of the American Institute of Chemical Engineers. He has served
the AIChE by participating in accreditation visits to departments of chemical engineer-

ing for ABET and by chairing sessions of the Department Heads Forum at the annual
meetings of AIChE.

xx ABOUT THE AUTHOR
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1
CHAPTER
1
I
n this chapter we examine the concept of chemical process control and introduce sev-
eral examples to illustrate the necessity for process modeling as we begin our study
of process dynamics and control.
1.1 WHY PROCESS CONTROL?
As competition becomes stiffer in the chemical marketplace and processes become
more complicated to operate, it is advantageous to make use of some form of automatic
control. Automatic control of a process offers many advantages, including
• Enhanced process safety
• Satisfying environmental constraints
• Meeting ever-stricter product quality specifications
• More efficient use of raw materials and energy
• Increased profitability
Considering all the benefits that can be realized through process control, it is well
worth the time and effort required to become familiar with the concepts and practices
used in the field.
1.2 CONTROL SYSTEMS
Control systems are used to maintain process conditions at their desired values by
manipulating certain process variables to adjust the variables of interest. A common
example of a control system from everyday life is the cruise control on an automobile.
The purpose of a cruise control is to maintain the speed of the vehicle (the controlled

variable) at the desired value (the set point) despite variations in terrain, hills, etc.
INTRODUCTORY
CONCEPTS
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2 CHAPTER 1 INTRODUCTORY CONCEPTS
(disturbances) by adjusting the throttle, or the fuel flow to the engine (the manipulated
variable). Another common example is the home hot water heater. The control system
on the hot water heater attempts to maintain the temperature in the tank at the desired
value by manipulating the fuel flow to the burner (for a gas heater) or the electrical
input to the heater in the face of disturbances such as the varying demand on the heater
early in the morning, as it is called upon to provide water for the daily showers. A third
example is the home thermostat. This control system is designed to maintain the tem-
perature in the home at a comfortable value by manipulating the fuel flow or electrical
input to the furnace. The furnace control system must deal with a variety of disturbances
to maintain temperature in the house, such as heat losses, doors being opened and hope-
fully closed, and leaky inefficient windows. The furnace must also be able to respond
to a request to raise the desired temperature if necessary. For example, we might desire
to raise the temperature by 5 Њ , and we’d like the system to respond smoothly and effi-
ciently. From these examples, we can deduce that there are several common attributes
of control systems:
• The ablity to maintain the process variable at its desired value in spite of distur-
bances that might be experienced (this is termed disturbance rejection )
• The ability to move the process variable from one setting to a new desired setting
(this is termed set point tracking )
Conceptually we can view the control systems we’ve discussed in the following
general manner ( Fig. 1–1 ).
The controller compares the measurement signal of the controlled variable to the
set point (the desired value of the controlled variable). The difference between the two
values is called the error.

Error Set point value Measurement siϭϪ()( ggnal of controlled variable)

Depending upon the magnitude and sign of the error, the controller takes appropriate
action by sending a signal to the final control element, which provides an input to the pro-
cess to return the controlled variable to the set point. The concept of using information
Process
Manipulated
Variable
Controller
Controlled
Variable
Measurement
Device
Desired Value
(Set Point)
Final
Control
Element
Disturbances
Control
Signal
Measurement
Signal
FIGURE 1–1
Generalized process control system.
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CHAPTER 1 INTRODUCTORY CONCEPTS 3
about the deviation of the system from its desired state to control the system is called

feedback control. Information about the state of the system is “fed back” to a controller,
which utilizes this information to change the system in some way.
The type of control system shown in Fig. 1–1 is termed a closed-loop feedback
control system. Closed-loop refers to the fact that the controller automatically acts to
return the controlled variable to its desired value. In contrast, an open-loop system
would have the measurement signal disconnected from the controller, and the control-
ler output would have to be manually adjusted to change the value of the controlled
variable. An open-loop system is sometimes said to be in manual mode as opposed to
automatic mode (closed-loop). Negative feedback is the most common type of sig-
nal feedback. Negative refers to the fact that the error signal is computed from the
difference between the set point and the measured signal. The negative value of the
measured signal is “fed back” to the controller and added to the set point to compute
the error.
Example 1.1. Hot water tank control system. As a specific example, let us
consider a hot water heater for a home ( Fig. 1–2 ) and examine its control system,
using the same type of diagram ( Fig. 1–3 ).
The desired hot water temperature is selected by the homeowner, and typi-
cally it is in the neighborhood of 120 to 140 Њ F. Let us assume that the set point is
130 Њ F. The thermocouple measures the temperature of the water in the tank and
sends a signal to the thermostat indicating the temperature. The thermostat (con-
troller) determines the error as

Error
set point measured
ϭϪTT

If the error is positive (Ͼ 0), the
measured temperature is lower than
desired and the thermostat opens the
fuel valve to the burner which adds

heat to the tank. If the error is zero or
negative (Յ 0), the thermostat closes
the fuel valve and no heat is added
to the tank. Disturbances to the sys-
tem, which decrease the tempera-
ture of the water in the tank, include
ambient heat losses and hot water
demand by the household which is
replaced with a cold water feed.
Types of Controllers
The thermostat on the hot water heater
is called an “on/off ” type of controller.
Depending on the value of the error
signal, the output from the controller is
FIGURE 1–2
Physical drawing of a hot water heater.
Hot
water
outlet
TPR valve
Anode
Thermostat
Drain
valve
Dip tube
Cold water
inlet
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4 CHAPTER 1 INTRODUCTORY CONCEPTS

either “full on” or “full off ” and the fuel valve is full open or full closed; there are no
intermediate values of the output. Many other types of controllers that we will study can
modulate their output based on the magnitude of the error signal, how long the error
signal has persisted, and even how rapidly the error appears to be changing.
Clearly, the larger the error, the less we are satisfied with the present state of
affairs and vice versa. In fact, we are completely satisfied only when the error is exactly
zero. Based on these considerations, it is natural to suggest that the controller should
change the heat input by an amount proportional to the error. This is called proportional
control. In effect, the controller is instructed to maintain the heat input at the steady-
state design value as long as the error is zero. If the tank temperature deviates from the
set point, causing an error, the controller is to use the magnitude of the error to change
the heat input proportionally. We shall reserve the right to vary the proportionality con-
stant to suit our needs. This degree of freedom forms a part of our instructions to the
controller. As we will see shortly during the course of our studies, the larger we make
the proportionality constant for the proportional controller (called the controller gain),
the smaller the steady-state error will become. We will also see that it is impossible to
completely eliminate the error through the use of a proportional controller. For example,
if the set point is 130 Њ F and a disturbance occurs that drops the temperature to 120 Њ F,
if we use only a proportional controller, then we will never be able to get the tank tem-
perature to exactly 130 Њ F. Once the sytem stabilizes again, the temperature will not be
exactly 130 Њ F, but perhaps 127ЊF or 133 Њ F. There will always be some residual steady-
state error (called offset ). For a home water heater, this is probably good enough; the
exact temperature is not that critical. In an industrial process, this may not be adequate,
and we have to resort to a bit more complicated controller to drive the error to zero.
Considerable improvement may be obtained over proportional control by adding
integral control. The controller is now instructed to change the heat input by an addi-
tional amount proportional to the time integral of the error. This type of control system
has two adjustable parameters: a multiplier for the error and a multiplier for the integral
of the error. If this type of controller is used, the steady-state error will be zero. From this
standpoint, the response is clearly superior to that of the system with proportional control

only. One price we pay for this improvement is the tendency for the system to be more
FIGURE 1–3
Block diagram of a hot water heater control system.
Hot
Water Tank
Heating
Process
Control Signal
to
Fuel Valve
Thermostat
Actual Hot
Water
Temperature
Thermocouple
Desired Hot
Water
Temperature
Indicated Hot
Water
Temperature
Fuel
Valve
Manipulated
Fuel Flow
to Burner
Disturbances
(heat losses, hot
water demand)
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